12 Questions
What is the alternative hypothesis (Ha) in this scenario?
po > pc
Which method involves choosing Test for difference in proportions and creating a randomization distribution?
P-value for randomization distribution
What is the P-value obtained from the normal distribution method when testing for the significance of the difference in proportions?
0.014
Which z-score was calculated indicating the significance of the difference in proportions using the Standard Normal Distribution method?
2.2
What does a P-value below the significance level alpha (0.05) indicate?
The organic food helps significantly
Which step involves leaving the mean at 0 and standard deviation at 1 in the process of testing for significance?
Standard Normal Distribution
What is the total area under a normal distribution curve?
1
What does a probability of 1 in a standard normal distribution indicate?
The event is certain to happen.
How can any normal distribution be converted to a standard normal distribution?
By using a specific formula
What does a mean of 0 indicate in a standard normal distribution?
The data is centered at 0
How does the distribution change as the sample size, n, increases in statistics?
It tends to more closely resemble a normal distribution
What phenomenon have we observed with randomization distributions using n=1000 in statkey?
The distribution tends towards normality
Study Notes
Normal Distribution
- The total area under the curve of a normal distribution is 1, which corresponds to a probability of 1.
- The standard normal distribution has a mean of 0 and a standard deviation of 1.
- Any normal distribution can be converted to a standard normal distribution using the formula: (x - μ) / σ.
Central Limit Theorem
- The Central Limit Theorem states that as the sample size (n) increases, the distribution tends to resemble a normal distribution.
Hypothesis Testing
- Example: A 16-year-old girl investigated the effect of organic food on fruit flies' longevity.
- Null hypothesis (Ho): po = pc (no difference in longevity between organic and conventional food)
- Alternative hypothesis (Ha): po > pc (organic food increases longevity)
Difference in Proportions
- The observed sample statistic: 318/500 - 285/500 = 0.066
- This difference is significant if the P-value is less than the chosen alpha level (0.05)
P-value Methods
- Randomization distribution: create a randomization distribution using Statkey, with 1000 samples, and calculate the P-value.
- Normal distribution: specify the mean and standard deviation of the normal distribution, and calculate the P-value using Statkey.
- Standard Normal Distribution: calculate the z-score, and then use Statkey to find the P-value.
Results
- All three methods (randomization distribution, normal distribution, and standard normal distribution) yield a P-value close to 0.02, indicating significant evidence that organic food helps increase the longevity of fruit flies.
Test your knowledge on normal distribution and standard normal distribution, including how to convert any normal distribution to a standard normal distribution. Explore probability calculations and understanding the relationship between mean, standard deviation, and the total area under the curve for a normal distribution.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
